We show the DFT band at \(E_z=0\)  in the left panel of Fig. 3(c), where the inset enlarges the local band near \(E_{\rm F}\)  and is well fitted by \(\Delta =8.9\)  meV, \(m_z=-7.2\)  meV, \(t=2.441\)  eV, \(\gamma =0.396\)  eV in our model and an additional interlayer next-nearest neighboring hopping \(\gamma ^{\prime }=0.267\)  eV.
Here, we have \(m_z<0\)  and \(\Delta >|m_z|\) , different from the assumptions in Fig. 2.
As expected, we show the contrasting spin polarization of the bands for \(E_z=\pm 0.2\)  V/nm, which is much smaller than 1\(\sim \) 3 V/nm experimentally accessible in vdW systems of BLG [1]} and bilayer CrI\(_3\)  [2]}. We plot the spin-dependent band gap \(E_g^s\)  versus \(E_z\)  in Fig. 3(d), where spin-up and spin-down band gaps vanish for \(E_z>0.23\)  V/nm and \(E_z<-0.1\)  V/nm, respectively. This is beyond our model because CGT has a nonnegligible contribution to \(E_g^s\)  as \(E_z\)  increases.
